176/175
176/175, the valinorsma, is a small 11-limit comma measuring about 9.9 cents. It is the amount by which 11/7 exceeds two 5/4's stacked, that is, the difference between 11/7 and 25/16, 8/7 and 25/22, 14/11 and 32/25, 15/11 and 48/35, or 22/15 and 35/24.
| Interval information |
Lorugugu comma
reduced
S22⋅S23⋅S24
176/175 factors neatly into two 13-limit superparticular commas: (352/351)(351/350).
Temperaments
Tempering out this comma leads to the rank-4 valinorsmic temperament (→ Rank-4 temperament #Valinorsmic (176/175)), or in the 2.5.7.11 subgroup, the valinor temperament, enabling valinorsmic chords. See Valinorsmic clan for the clan of rank-3 temperaments where it is tempered out.
Etymology
The name seems to originally have been a portmanteau of "valentine", "orwell", and possibly an additional temperament, all of which temper out this comma in the 11-limit, as was a common custom for naming commas. However, the name has been re-interpreted as referring to "Valinor", a location in J. R. R. Tolkien's Middle-earth, and various temperaments in the valinorsmic clan have been named after the Valar, that realm's inhabitants.